Arc length

Arc length of one arch is , where is radius of the rolling circle. Units of measurements are the same as axis units.
For different values of c you get a various type of cycloid.
  • Curtate cycloid: Here the point tracing out the curve is inside the circle, which rolls on a line.
  • Prolate cycloid: Here the point tracing out the curve is outside the circle, which rolls on a line.

When rectified, the curve gives a straight line segment with the same length as the curve's arc length.